Impacts of diapause eggs on mosquito population suppression based on incompatible or sterile insect technique

Mosquito -borne diseases kill more than 700, 000 people a year, and the toll continues to rise. Controlling mosquito population is the key measure to prevent mosquito -borne diseases. Releasing sterile male mosquitoes to suppress wild mosquito population is an environmentally friendly and efficient method, which has been proven to successfully eliminate wild mosquitoes in laboratory, but it is difficult to achieve such effectiveness in the field. The diapause of mosquito eggs is considered an important factor hindering mosquito population suppression. In this paper, we formulate an ordinary differential equation model to discuss the impact of diapause eggs on mosquito population suppression. We prove that there exists at most one periodic solution in our model, and obtain sufficient and necessary conditions for the existence of an unique periodic solution. We give numerical simulations to confirm our theoretical results.